# Some Fundamental Theorems in Mathematics

@article{Knill2018SomeFT, title={Some Fundamental Theorems in Mathematics}, author={Oliver Knill}, journal={arXiv: History and Overview}, year={2018} }

An expository hitchhikers guide to some theorems in mathematics. Criteria for the current list of 135 theorems are whether the result can be formulated elegantly, whether it is beautiful or useful and whether it could serve as a guide [5] without leading to panic. The order is not a ranking but more like a time-line when things were written down. Since [280] stated “a mathematical theorem only becomes beautiful if presented as a crown jewel within a context” we try sometimes to give some…

## One Citation

The Relationship between Constructive Real Numbers and Left Number in Constructive Mathematics

- MathematicsJournal of Physics: Conference Series
- 2022

Generally, construction real numbers are considered constructive real numbers that coherently relate to some construction approaches. The analysis of this paper primarily focuses on the perspectives…

## References

SHOWING 1-10 OF 812 REFERENCES

An Introduction to the Theory of Numbers

- MathematicsNature
- 1946

THIS book must be welcomed most warmly into X the select class of Oxford books on pure mathematics which have reached a second edition. It obviously appeals to a large class of mathematical readers.…

A Refinement of a Theorem of J. E. Littlewood

- PhilosophyAm. Math. Mon.
- 2014

A corrected and refined version of Littlewood’s theorem is proposed, which proves that two sentences is a lower bound for any thesis in mathematics, and shows that this lower bound could in theory be attained by exhibiting a one-sentence proof of Picard's “small” theorem.

Rudiments of Ramsey theory

- Mathematics
- 1981

It is no exaggeration to say that over the past several decades there has been a veritable explosion of activity in the general field of combinatorics. Ramsey theory, in particular, has shown…

An Elementary Treatise on Pure Geometry, with numerous examples

- ArtNature
- 1893

THE opening sentence of the Preface—“The author has attempted to bring together all the well-known theorems and examples connected with Harmonics, Anharmonics, Involution, Projection (including…

A Brief History of Mathematics

- HistoryNature
- 1900

THANKS, in great measure, to the unwearied industry and acumen of Dr. Moritz Cantor, it is now comparatively easy to construct a synopsis of mathematical history down to the beginning of the…

Men of Mathematics

- ArtNature
- 1937

The amount of biographical details and of mathematics that the writer has compressed into a volume of 650 pages is extraordinary ; but he is never dull ; his style is lively, at times even 'snappy' ; he carries the reader along ; he whets the appetite.

The Pythagorean Theorem: The Story of Its Power and Beauty, by Alfred S. Posamentier

- Art
- 2011

In the introduction, the author states, ‘. . ., this famous theorem which we clearly associate with geometry, is also the basis for the field of trigonometry and finds its way into countless other…

Elements of Mathematics: From Euclid to Gödel

- Mathematics, Art
- 2016

Elements of Mathematics takes readers on a fascinating tour that begins in elementary mathematics--but, as John Stillwell shows, this subject is not as elementary or straightforward as one might…

Princeton companion to mathematics

- Art
- 2008

This is a one-of-a-kind reference for anyone with a serious interest in mathematics. Edited by Timothy Gowers, a recipient of the Fields Medal, it presents nearly two hundred entries, written…

The Four-Color Problem

- Mathematics
- 1978

A new and interesting type of theorem has appeared, one which has no proof of the traditional type; the correctness of the proof cannot be checked without the aid of a computer; the crucial ideas were perfected by computer experiments.